%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU630^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:25 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 4
% Syntax : Number of formulae : 61 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 697 ( 214 equ; 0 cnn)
% Maximal formula atoms : 8 ( 11 avg)
% Number of connectives : 998 ( 78 ~; 94 |; 61 &; 713 @)
% ( 5 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 30 usr; 15 con; 0-4 aty)
% ( 0 !!; 19 ??; 0 @@+; 0 @@-)
% Number of variables : 229 ( 54 ^; 145 !; 30 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
powerset: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_5,type,
dsetconstrI: $o ).
thf(func_def_7,type,
binunion: $i > $i > $i ).
thf(func_def_8,type,
kpair: $i > $i > $i ).
thf(func_def_9,type,
cartprod: $i > $i > $i ).
thf(func_def_10,type,
ubforcartprodlem3: $o ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_26,type,
sK5: $i > $o ).
thf(func_def_32,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X1: $i > $o,X0: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(f3,axiom,
( cartprod
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
@ ^ [X2: $i] :
? [X3: $i] :
( ? [X4: $i] :
( ( X2
= ( kpair @ X3 @ X4 ) )
& ( in @ X4 @ X1 ) )
& ( in @ X3 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprod) ).
thf(f4,axiom,
( ubforcartprodlem3
= ( ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(f5,conjecture,
( dsetconstrI
=> ( ubforcartprodlem3
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
thf(f6,negated_conjecture,
~ ( dsetconstrI
=> ( ubforcartprodlem3
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
~ ( dsetconstrI
=> ( ubforcartprodlem3
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( kpair @ X1 @ X3 ) @ ( cartprod @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
~ ( ( dsetconstrI = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( $true
= ( in @ ( kpair @ X1 @ X3 ) @ ( cartprod @ X0 @ X2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( ubforcartprodlem3
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X0 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
( ( ubforcartprodlem3 = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( in @ ( kpair @ X0 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f12,plain,
( cartprod
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
@ ^ [X2: $i] :
? [X3: $i] :
( ? [X4: $i] :
( ( X2
= ( kpair @ X3 @ X4 ) )
& ( in @ X4 @ X1 ) )
& ( in @ X3 @ X0 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
( cartprod
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( kpair @ Y3 @ Y4 )
= Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ( ( X0 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[],[f1]) ).
thf(f15,plain,
( ( dsetconstrI = $true )
<=> ! [X2: $i,X1: $i,X0: $i > $o] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( $true
= ( X0 @ X2 ) )
=> ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
( ( dsetconstrI = $true )
<=> ! [X2: $i,X1: $i,X0: $i > $o] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true
!= ( X0 @ X2 ) )
| ( ( in @ X2 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f17,plain,
( ! [X1: $i,X0: $i > $o,X2: $i] :
( ( $true
!= ( X0 @ X2 ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
<=> ( dsetconstrI = $true ) ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
( ( ubforcartprodlem3 = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ! [X3: $i] :
( ( ( in @ ( kpair @ X0 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) )
= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f19,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X1 @ X3 ) @ ( cartprod @ X0 @ X2 ) ) )
& ( $true
= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X1 @ X0 ) ) )
& ( ubforcartprodlem3 = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f20,plain,
( ( ubforcartprodlem3 = $true )
& ( dsetconstrI = $true )
& ? [X0: $i,X2: $i,X1: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X1 @ X3 ) @ ( cartprod @ X0 @ X2 ) ) )
& ( $true
= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X1 @ X0 ) ) ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
( ( ubforcartprodlem3 = $true )
& ( dsetconstrI = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) ) ),
inference(rectify,[],[f20]) ).
thf(f22,plain,
( ( ubforcartprodlem3 = $true )
& ( dsetconstrI = $true )
& ( $true
!= ( in @ ( kpair @ sK2 @ sK3 ) @ ( cartprod @ sK0 @ sK1 ) ) )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( ( in @ sK2 @ sK0 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f21]) ).
thf(f23,plain,
( ( ! [X1: $i,X0: $i > $o,X2: $i] :
( ( $true
!= ( X0 @ X2 ) )
| ( ( in @ X2 @ X1 )
!= $true )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X1: $i,X0: $i > $o,X2: $i] :
( ( $true
= ( X0 @ X2 ) )
& ( ( in @ X2 @ X1 )
= $true )
& ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f17]) ).
thf(f24,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
= ( X4 @ X5 ) )
& ( $true
= ( in @ X5 @ X3 ) )
& ( $true
!= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f25,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ( ( $true
= ( sK5 @ sK6 ) )
& ( $true
= ( in @ sK6 @ sK4 ) )
& ( $true
!= ( in @ sK6
@ ( dsetconstr @ sK4
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4),skolemize(X4,sK5),skolemize(X5,sK6)],[f24]) ).
thf(f26,plain,
( ( ( ubforcartprodlem3 = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ? [X3: $i] :
( ( ( in @ ( kpair @ X0 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) )
!= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X0 @ X2 )
= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ! [X3: $i] :
( ( ( in @ ( kpair @ X0 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X2 @ X1 ) ) ) )
= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( ubforcartprodlem3 != $true ) ) ),
inference(nnf_transformation,[],[f18]) ).
thf(f27,plain,
( ( ( ubforcartprodlem3 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X0 ) ) ) ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ X1 )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ! [X7: $i] :
( ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ ( powerset @ ( powerset @ ( binunion @ X5 @ X4 ) ) ) ) )
| ( $true
!= ( in @ X7 @ X4 ) ) )
| ( ( in @ X6 @ X5 )
!= $true ) )
| ( ubforcartprodlem3 != $true ) ) ),
inference(rectify,[],[f26]) ).
thf(f28,plain,
( ( ( ubforcartprodlem3 = $true )
| ( ( $true
!= ( in @ ( kpair @ sK9 @ sK10 ) @ ( powerset @ ( powerset @ ( binunion @ sK8 @ sK7 ) ) ) ) )
& ( $true
= ( in @ sK10 @ sK7 ) )
& ( $true
= ( in @ sK9 @ sK8 ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ! [X7: $i] :
( ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ ( powerset @ ( powerset @ ( binunion @ X5 @ X4 ) ) ) ) )
| ( $true
!= ( in @ X7 @ X4 ) ) )
| ( ( in @ X6 @ X5 )
!= $true ) )
| ( ubforcartprodlem3 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10)],[f27]) ).
thf(f29,plain,
( cartprod
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( kpair @ Y3 @ Y4 )
= Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f30,plain,
( ( in @ sK2 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f31,plain,
( $true
= ( in @ sK3 @ sK1 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f32,plain,
( $true
!= ( in @ ( kpair @ sK2 @ sK3 ) @ ( cartprod @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
dsetconstrI = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f34,plain,
ubforcartprodlem3 = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f39,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
!= $true )
| ( dsetconstrI != $true )
| ( $true
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f40,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ ( powerset @ ( powerset @ ( binunion @ X5 @ X4 ) ) ) ) )
| ( $true
!= ( in @ X7 @ X4 ) )
| ( ( in @ X6 @ X5 )
!= $true )
| ( ubforcartprodlem3 != $true ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f45,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true
= ( in @ X2 @ ( dsetconstr @ X0 @ X1 ) ) )
| ( ( in @ X2 @ X0 )
!= $true )
| ( dsetconstrI != $true )
| ( ( X1 @ X2 )
!= $true ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f49,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true
= ( in @ X2 @ ( dsetconstr @ X0 @ X1 ) ) )
| ( ( X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f45,f33]) ).
thf(f54,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ ( powerset @ ( powerset @ ( binunion @ X5 @ X4 ) ) ) ) )
| ( ( in @ X6 @ X5 )
!= $true )
| ( $true
!= ( in @ X7 @ X4 ) ) ),
inference(forward_subsumption_resolution,[],[f40,f34]) ).
thf(f58,plain,
! [X1: $i] :
( ( cartprod @ X1 )
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( ( kpair @ Y3 @ Y4 )
= Y2 ) ) ) ) ) )
@ X1 ) ),
inference(argument_congruence,[],[f29]) ).
thf(f59,plain,
! [X1: $i] :
( ( cartprod @ X1 )
= ( ^ [Y0: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X1 @ Y0 ) ) )
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ( kpair @ Y2 @ Y3 )
= Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X1 @ Y0 ) ) )
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ( kpair @ Y2 @ Y3 )
= Y1 ) ) ) ) ) )
@ X2 )
= ( cartprod @ X1 @ X2 ) ),
inference(argument_congruence,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X1: $i] :
( ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) ) )
= ( cartprod @ X1 @ X2 ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) )
@ X2 ) )
| ( $true
= ( in @ X2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ),
inference(superposition,[],[f49,f61]) ).
thf(f63,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
& ( ( kpair @ Y0 @ Y1 )
= X2 ) ) ) ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
& ( ( kpair @ Y0 @ Y1 )
= X2 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( ( in @ X3 @ X0 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( ( kpair @ X3 @ Y0 )
= X2 ) ) ) )
= $false )
| ( $true
= ( in @ X2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) )
| ( $true
= ( in @ X2 @ ( cartprod @ X0 @ X1 ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( ( kpair @ X3 @ Y0 )
= X2 ) ) )
= $false )
| ( ( in @ X3 @ X0 )
= $false ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ X2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( ( kpair @ X3 @ Y0 )
= X2 ) )
@ X4 )
= $false )
| ( ( in @ X3 @ X0 )
= $false ) ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ X2 @ ( cartprod @ X0 @ X1 ) ) )
| ( ( ( in @ X4 @ X1 )
& ( ( kpair @ X3 @ X4 )
= X2 ) )
= $false )
| ( $true
!= ( in @ X2 @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) )
| ( ( in @ X3 @ X0 )
= $false ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ X2 @ ( cartprod @ X0 @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) )
| ( ( ( kpair @ X3 @ X4 )
= X2 )
= $false )
| ( ( in @ X3 @ X0 )
= $false )
| ( ( in @ X4 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) ) ) )
| ( ( in @ X3 @ X0 )
= $false )
| ( ( in @ X4 @ X1 )
= $false )
| ( ( kpair @ X3 @ X4 )
!= X2 )
| ( $true
= ( in @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X5 @ X3 )
= $false )
| ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ ( cartprod @ X2 @ X3 ) ) )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X4 @ X2 )
= $false )
| ( $true
!= ( in @ X1 @ X3 ) )
| ( ( kpair @ X0 @ X1 )
!= ( kpair @ X4 @ X5 ) ) ),
inference(superposition,[],[f70,f54]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( ( kpair @ X0 @ X1 )
!= ( kpair @ X4 @ X5 ) )
| ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ ( cartprod @ X2 @ X3 ) ) )
| ( ( in @ X4 @ X2 )
= $false )
| ( $true
!= ( in @ X1 @ X3 ) )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X5 @ X3 )
= $false ) ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ ( cartprod @ X2 @ X3 ) ) )
| ( ( in @ X1 @ X3 )
= $false )
| ( $true
!= ( in @ X1 @ X3 ) )
| ( ( in @ X0 @ X2 )
= $false )
| ( ( in @ X0 @ X2 )
!= $true ) ),
inference(equality_resolution,[],[f72]) ).
thf(f74,plain,
( ( $true != $true )
| ( ( in @ sK2 @ sK0 )
= $false )
| ( ( in @ sK2 @ sK0 )
!= $true )
| ( ( in @ sK3 @ sK1 )
= $false )
| ( $true
!= ( in @ sK3 @ sK1 ) ) ),
inference(superposition,[],[f32,f73]) ).
thf(f75,plain,
( ( ( in @ sK3 @ sK1 )
= $false )
| ( ( in @ sK2 @ sK0 )
= $false )
| ( $true
!= ( in @ sK3 @ sK1 ) )
| ( ( in @ sK2 @ sK0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f76,plain,
( ( ( in @ sK3 @ sK1 )
= $false )
| ( ( in @ sK2 @ sK0 )
!= $true )
| ( ( in @ sK2 @ sK0 )
= $false ) ),
inference(forward_subsumption_resolution,[],[f75,f31]) ).
thf(f77,plain,
( ( ( in @ sK3 @ sK1 )
= $false )
| ( ( in @ sK2 @ sK0 )
= $false ) ),
inference(forward_subsumption_resolution,[],[f76,f30]) ).
thf(f78,plain,
( ( $true = $false )
| ( ( in @ sK2 @ sK0 )
= $false ) ),
inference(forward_demodulation,[],[f77,f31]) ).
thf(f79,plain,
( ( in @ sK2 @ sK0 )
= $false ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f81,plain,
$true = $false,
inference(superposition,[],[f30,f79]) ).
thf(f82,plain,
$false,
inference(trivial_inequality_removal,[],[f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU630^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n014.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:00:11 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.27 % (2707025)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (2707032)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3616977481:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.27 % (2707032)Instruction limit reached!
% 0.21/0.27 % (2707032)------------------------------
% 0.21/0.27 % (2707032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (2707032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (2707032)CaDiCaL version: 2.1.3
% 0.21/0.27 % (2707032)Termination reason: Instruction limit
% 0.21/0.27 % (2707032)Termination phase: Saturation
% 0.21/0.27 % (2707032)Time elapsed: 0.001 s
% 0.21/0.27 % (2707032)Peak memory usage: 12 MB
% 0.21/0.27 % (2707032)Instructions burned: 4 (million)
% 0.21/0.27 % (2707036)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.27 % (2707036)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.27 % (2707030)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1067337857:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (2707033)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=441891470:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.27 % (2707031)lrs+10_16_si=on:nwc=1.5:random_seed=2731195440:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (2707034)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2521773712:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.27 % (2707035)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1469633430:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.27 % (2707036)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2170675804:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.27 % (2707038)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2084573664:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.27 % (2707038)Instruction limit reached!
% 0.21/0.27 % (2707038)------------------------------
% 0.21/0.27 % (2707038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (2707038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (2707038)CaDiCaL version: 2.1.3
% 0.21/0.27 % (2707038)Termination reason: Instruction limit
% 0.21/0.27 % (2707038)Termination phase: Saturation
% 0.21/0.27 % (2707038)Time elapsed: 0.001 s
% 0.21/0.27 % (2707038)Peak memory usage: 12 MB
% 0.21/0.27 % (2707038)Instructions burned: 3 (million)
% 0.21/0.27 % (2707031) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2707025-2707031"...
% 0.21/0.27 % (2707034) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2707025-2707034"...
% 0.21/0.27 % (2707034)...printing done.
% 0.21/0.27 % (2707031)...printing done.
% 0.21/0.27 % (2707034)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (2707034)------------------------------
% 0.21/0.27 % (2707034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (2707034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (2707034)CaDiCaL version: 2.1.3
% 0.21/0.27 % (2707034)Termination reason: Refutation
% 0.21/0.27 % (2707034)Time elapsed: 0.008 s
% 0.21/0.27 % (2707034)Peak memory usage: 12 MB
% 0.21/0.27 % (2707034)Instructions burned: 14 (million)
% 0.21/0.27 % (2707025)Success in time 0.04 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------